In our everyday lives we are not aware of the Earth's motion. When we play crazy-golf, we do not care that the Earth's momentary velocity due to its solar obit is some 30 kilometers per second (0.00001c), or that the velocity due to the galaxy's rotation is a little over around 200 kilometers per second (~0.00006c) ... as far as we are concerned, we are not moving at all. This idea that the simple velocity of systems moving in straight lines at constant velocities had no effect on interior physics became known as the "special" (for "special case") or "restricted" theory of relativity. Although we couldn't tell if we were moving or not in these simple cases, when we accelerated or were fixed to a rotating body, we could tell that we were accelerated or rotating due to experiencing gee-forces.
Newtonian physics treated these complex motions as absolute rather than relative, because they had absolute measurable consequences (like the reading on an accelerometer). George Berkeley criticised Newton's schema for classifying absolute motions, and in the C19th Ernst Mach explained that we could apply the relativity principle generally, if only we treated gee-forces as real gravitational fields, caused by the relative motion of the background stars.
According to the general principle of relativity ("GPoR"), just as we felt gravitational effects when there was acceleration or rotation with respect to the distant stars, so there should also be corresponding gravitational side-effects when there was any relative acceleration or rotation between any two masses whatsoever. When a racing-car accelerates, its accelerating mass should produce a tiny tug on nearby bystanders, and when we approach a playground roundabout, we should feel an inward attraction due to its spin, and also a sideways dragging effect.
These dragging effects due to moving masses are examples of something called gravitomagnetism. Gravitomagnetism can be considered the basic expression of the GPoR as physics. Without gravitomagnetism, we don't have the GPoR, or a general theory of relativity.
when neighbouring masses are accelerated, and, in fact, the force must be in the same direction as that acceleration.
A rotating hollow body must generate inside of itself a "Coriolis field", which defects moving bodies in the sense of the rotation, and a radial centrifugal field as well.
... these ... effects ... which are to be expected in accordance with Mach's ideas, are actually present according to our theory ...